{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "73bd968b-d970-4a05-94ef-4e7abf990827",
   "metadata": {},
   "source": [
    "Chapter 22\n",
    "\n",
    "# 三维向量\n",
    "Book_3《数学要素》 | 鸢尾花书：从加减乘除到机器学习 (第二版)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "12e8a063-9a11-4028-aa74-8a2f3f758f43",
   "metadata": {},
   "source": [
    "这段代码在三维空间中可视化了向量的绘制和表示。它首先定义了几个向量：向量$$\\vec{c} = \\begin{bmatrix} 4 \\\\ 3 \\\\ 5 \\end{bmatrix}$$、向量$$\\vec{a} = \\begin{bmatrix} 4 \\\\ 3 \\\\ 0 \\end{bmatrix}$$以及标准单位向量$$\\vec{i} = \\begin{bmatrix} 1 \\\\ 0 \\\\ 0 \\end{bmatrix}$$、$$\\vec{j} = \\begin{bmatrix} 0 \\\\ 1 \\\\ 0 \\end{bmatrix}$$和$$\\vec{k} = \\begin{bmatrix} 0 \\\\ 0 \\\\ 1 \\end{bmatrix}$$。\n",
    "\n",
    "代码中的函数`draw_vector`用于绘制从原点出发的向量。对于每个向量，该函数绘制其方向，并在向量的末端添加标签，标明向量的名称及其具体坐标。通过$plt.quiver$函数实现三维箭头的绘制，以表示每个向量的方向和长度。此外，代码为各向量指定了不同的颜色，使得它们在图中清晰可分。\n",
    "\n",
    "三维坐标系的范围设置为$x$、$y$和$z$轴都在$[0, 5]$之间，轴标签分别为$x$、$y$和$z$。最终，该可视化设置了$20^\\circ$的仰角和$60^\\circ$的方位角来观察三维图形，使得各向量在空间中的位置和方向更加清晰。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "10ecf35d-a5ed-4b2a-a47c-806cadc6872b",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "70a662e6-61aa-4855-9cd2-28433a3f2692",
   "metadata": {},
   "source": [
    "## 绘制向量函数"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "b8ebf4a8-5b6a-44e7-9b6f-e086a7135352",
   "metadata": {},
   "outputs": [],
   "source": [
    "def draw_vector(ax, vector, color, label):\n",
    "    \"\"\"\n",
    "    绘制3D向量并添加标签\n",
    "    参数:\n",
    "    - ax: 3D子图对象\n",
    "    - vector: 向量数组，形如 [x, y, z]\n",
    "    - color: 向量颜色\n",
    "    - label: 向量标签\n",
    "    \"\"\"\n",
    "    ax.quiver(0, 0, 0, vector[0], vector[1], vector[2],\n",
    "              color=color, arrow_length_ratio=0.1, normalize=False)\n",
    "    label_text = f\"{label} ({vector[0]}, {vector[1]}, {vector[2]})\"\n",
    "    ax.text(vector[0], vector[1], vector[2], label_text,\n",
    "            color=color, verticalalignment='center')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3d6bf848-d64c-46f2-bc94-ace94ad0781f",
   "metadata": {},
   "source": [
    "## 定义向量"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "4f7d4795-2334-42c3-abf1-5b2836135633",
   "metadata": {},
   "outputs": [],
   "source": [
    "c = np.array([4, 3, 5])  # 向量 c\n",
    "a = np.array([4, 3, 0])  # 向量 a\n",
    "i = np.array([1, 0, 0])  # 单位向量 i\n",
    "j = np.array([0, 1, 0])  # 单位向量 j\n",
    "k = np.array([0, 0, 1])  # 单位向量 k"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "78141d0f-908e-4e6a-a991-feaa59d9e580",
   "metadata": {},
   "source": [
    "## 可视化"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "99a31db1-b7c4-4682-a12a-6b531f694eb7",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure()\n",
    "ax = plt.axes(projection='3d')\n",
    "\n",
    "# 绘制向量\n",
    "draw_vector(ax, a, 'blue', 'a')  # 向量 a\n",
    "draw_vector(ax, c, 'green', 'c')  # 向量 c\n",
    "draw_vector(ax, i, 'red', 'i')  # 单位向量 i\n",
    "draw_vector(ax, j, 'purple', 'j')  # 单位向量 j\n",
    "draw_vector(ax, k, 'orange', 'k')  # 单位向量 k\n",
    "\n",
    "# 设置正交投影\n",
    "ax.set_proj_type('ortho')\n",
    "\n",
    "# 设置坐标范围\n",
    "ax.set_xlim(0, 5)\n",
    "ax.set_ylim(0, 5)\n",
    "ax.set_zlim(0, 5)\n",
    "\n",
    "# 添加坐标轴标签\n",
    "ax.set_xlabel(r'$\\it{x}$')\n",
    "ax.set_ylabel(r'$\\it{y}$')\n",
    "ax.set_zlabel(r'$\\it{z}$')\n",
    "\n",
    "# 设置视角\n",
    "ax.view_init(azim=60, elev=20)\n",
    "\n",
    "# 显示网格样式\n",
    "ax.xaxis._axinfo[\"grid\"].update({\"linewidth\": 0.25, \"linestyle\": \":\"})\n",
    "ax.yaxis._axinfo[\"grid\"].update({\"linewidth\": 0.25, \"linestyle\": \":\"})\n",
    "ax.zaxis._axinfo[\"grid\"].update({\"linewidth\": 0.25, \"linestyle\": \":\"})\n",
    "\n",
    "plt.tight_layout()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "85a80909-2aac-49ed-bb7a-f8cc6b80ee7d",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "ecd322f4-f919-4be2-adc3-69d28ef25e69",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.12.7"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}
